Predator-prey models with delay and prey harvesting |
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Authors: | Annik Martin Shigui Ruan |
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Affiliation: | (1) Department of Mathematics, University of New Orleans, New Orleans, LA 70148-2900, USA, US;(2) Department of Mathematics and Statistics, Dalhousie University, Halifax, Nova Scotia, Canada. B3H 3J5. e-mail: ruan@mathstat.dal.ca, CA |
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Abstract: | It is known that predator-prey systems with constant rate harvesting exhibit very rich dynamics. On the other hand, incorporating time delays into predator-prey models could induce instability and bifurcation. In this paper we are interested in studying the combined effects of the harvesting rate and the time delay on the dynamics of the generalized Gause-type predator-prey models and the Wangersky-Cunningham model. It is shown that in these models the time delay can cause a stable equilibrium to become unstable and even a switching of stabilities, while the harvesting rate has a stabilizing effect on the equilibrium if it is under the critical harvesting level. In particular, one of these models loses stability when the delay varies and then regains its stability when the harvesting rate is increased. Computer simulations are carried to explain the mathematical conclusions. Received: 1 March 2000 / Revised version: 7 September 2000 /?Published online: 21 August 2001 |
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Keywords: | Mathematics Subject Classification (2000): 34K20 92D25 |
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